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Paper Information

Journal:   JOURNAL OF MATHEMATICAL EXTENSION   2018 , Volume 12 , Number 1; Page(s) 1 To 11.

A Generalization of Clique Polynomials and Graph Homomorphism

Author(s):  TEIMOORI H.*, BAYAT M.
* Department of Mathematics and Computer Science, Allameh Tabatabai University Tehran, iran
The clique polynomial of a graph G is the ordinary generating function of the number of complete subgraphs (cliques) of G. In this paper, we introduce a new vertex-weighted version of these polynomials. We also show that these weighted clique polynomials have always a real root provided that the weights are non-negative real numbers. As an application, we obtain a no-homomorphism criteria based on the largest real root of our vertex-weighted clique polynomial.
Keyword(s): Weighted clique polynomial,blow-up graph,No-Homomorphism criteria
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